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"The Day the Earth Stood Cool" (also known as "The Day the Earth Stayed Cool") is the seventh episode of Season 24.
Homer befriends Terrence (Fred Armisen) and Emily (Carrie Brownstein), new neighbors from Portland. Homer becomes like Terrence because he wants a younger, hipper image. When Bart gets into a fight with Terrance and Emily's son T-Rex (Patton Oswalt), the friendship becomes strained and Terrence, ticked off at the Simpsons, calls his friends from Portland, and Springfield is soon full with 'cool' people. Meanwhile, Marge feels uncomfortable around Emily and her friends when they are breastfeeding, and she is feeding Maggie from the bottle.
Homer becomes upset when someone believes him to be Bart's grandfather, and worries that he is no longer cool. He then meets Terrance, a cool donut chef from Portland, who is looking for a new place for him and his family to live as he believes Portland has been "played out". When he tells Homer that he sees potential in Springfield, Homer suggests he buy the house next door to his, which he does.
The Simpsons meet Terrance's wife Emily, his pet Armadillo Chuey, their daughter Corduroy and their son T-Rex, and get their first exposure to their way of life. While Homer and Lisa are immediately taken with the family, Bart is irritated by T-Rex's negative attitude and Marge is uncomfortable in their presence, particularly of Emily's public breastfeeding. Despite this Marge supports Homer in his desire to fit in with their lifestyle, and allows him to combine their yard with the neighbor's one into a "mono-yard" and lets him, Bart and Lisa to accompany Terrance and T-Rex to rock shows, Mexican wrestling, roller derby, Korean gangster films and Modern Art exhibitions, even though she grows concerned that the kids are becoming pretentious. The Simpsons are invited to T-Rex's birthday party, where Marge makes enemies of Emily and her fellow nursing mother friends by refusing to breast-feed Maggie. Meanwhile T-Rex mocks Homer's present and calls him a poser, which angers Bart and he starts a fight with him. This causes friction between the families (Homer is not invited to go midnight bike-riding), but when Bart explains himself Homer chooses to sever all ties with Terrance and his family.
Homer and Marge pressure Terrance and Emily to leave Springfield, but their "humble-bragging" of the town results in more cool people moving to Springfield. Their lifestyle quickly consumes the town; the Tire Fire becomes a Farmer's Market, the Android's Dungeon becomes a Taschen, King Toot's Music Store becomes King Toke's Medicinal Marijuana Center, Springfield Elementary becomes a co-op, and the Kwik-E-Mart turns into Apu's House of Spats. Meanwhile, Bart makes up with T-Rex and invites him to watch TV with him. Excited by the prospect, he abandons his compost-turning duties and joins Bart. The unturned compost, however, catches fire and starts to spread. Homer and Terrance work together to put out the fire using large drums of baby formula Marge keeps in the garage.
Shortly after, the New York Times names Springfield 'America's Coolest City', which makes it played out. Immediately upon hearing this, Terrance and Emily and the rest of the cool people move out of town, much to Lisa's dismay.